Higher order spectra, equivariant Hodge-Deligne polynomials and Macdonald type equations

TL;DR

This paper introduces higher order spectra for complex quasi-projective manifolds with finite group actions, providing refined invariants and Macdonald type equations to understand their structure.

Contribution

It defines new notions of higher order spectra and their refinements for manifolds with group actions, along with deriving Macdonald type equations for these invariants.

Findings

Defined higher order spectra for G-manifolds

Established Macdonald type equations for these spectra

Provided refinements of the spectra with automorphisms

Abstract

We define notions of higher order spectra of a complex quasi-projective manifold with an action of a finite group $G$ and with a $G$-equivariant automorphism of finite order, some of their refinements and give Macdonald type equations for them.